Plot hole: Vaughan discovers Lauren is a mole when he goes through her briefcase and discovers the wig, gun and fake passport she used in Germany a few hours before - surely even the worst secret agent in the world would have enough sense to get rid of such incriminating evidence as soon as possible, and not carry it back to the USA (sneaking it onto a plane, presumably) and leaving it in the room where the man you're lying to sleeps. Lauren is a highly skilled agent, if the Covenant selected her for a mission this important, so it's out of character (without an explanation) for her to be so sloppy.
Other mistake: When Jack logs into Lauren's e-mail account, for one, the birth dates on Lauren's IDs say 1959 and 69 (which would make her either 33 or 44). Plus you can see (possibly) real e-mails from actual crewmembers, for example at the bottom you can see "FW:Photos for Alias Ep.#315." (00:10:57)